Functional near infrared spectroscopy (fNIRS) is an emerging non-invasive imaging technique to assess the brain function. The technique is non-invasive and portable and therefore applicable in studies of children and toddlers especially those with neurodevelopmental disorders. fNIRS measurements are based on the local changes in cerebral hemodynamic levels (oxy-hemoglobin and deoxy-hemoglobin) associated with brain activity. Due to the low optical absorption of biological tissues at NIR wavelengths (700-900 nm), NIR light can penetrate deep enough to probe the cortical regions up to 1-3 cm deep. As mentioned above, the NIR absorption spectrum of the tissue is sensitive to changes in the concentration of major tissue chromophores, such as hemoglobin. Therefore, measurements of temporal variations of backscattered light can capture functionally evoked changes in the outermost cortex and can be used to assess the brain function. However, there is a need to address the changes in NIRS signal in relation with underlying physiological processes in brain such as cerebral autoregulation. In short, mechanism of cerebral autoregulation maintains the blood flow over the range of arterial blood pressure and due to high metabolic demand of neurons it becomes a vital process for a brain function. Devising a novel method of data processing to enrich informational content of measured characteristics from fNIRS is therefore crucial for further studies of brain function and development. In the current study, we introduced the novel parameter, Oxygenation Variability index (OV Index), directly obtained from fNIRS data to quantify the changes in oxygen saturation at frequencies related to cerebral autoregulation (CA). In our study we use two frequency bands (<0.1 Hz, related to process of cerebral autoregulation and 0.2-0.3 Hz, related to dynamic of respiration to examine the changes in OV index with age in group of typically developing children. We hypothesize that the OV index will reveal differences based on chronological age as seen in the extant literature on cerebral hemodynamics in children during the performance of the functional task. We first investigated the relationship between age and OV Index, for frequencies <0.1 Hz, during the ask, and rest conditions and found a significant quadratic relationship, for frequencies <0.1 Hz, across task F(14) = 10.6, p = 0.006. We investigated both linear and nonlinear trends for the respiration frequencies (.2-.3 Hz), and found no significant change of OV index with age Linear: F(15) = 0.98, p = 0.34; Quadratic: F(14) = 0.01, p = 0.91. The OV index values were higher for frequencies <0.1 Hz, for Task when compared to rest F(16) = 5.3, p = 0.04, F(16) = 8.3, p = 0.01, respectively. This finding is in line with those showing increases in efficiency of CA during completion of cognitive tasks (Panerai et al., 2005). Furthermore, we have extended our analysis to children and toddler in both typical and language delay group between age of 18-36 months old to better understand the physiological development and impairments related to language delay at the early age. We have also examined the brain function using other non-invasive methods such as electroencephalogram (EEG) to examine the functional connectivity in brain. We have employed a new approach to trace the dynamic patterns of human brain task-based functional connectivity with EEG. The EEG signals of 5 healthy subjects were recorded while they performed an auditory oddball and a visual modified oddball tasks. To capture the dynamic patterns of functional connectivity during the execution of each task, EEG signals are segmented into duration that correspond to the temporal windows of previously well-studied event-related potentials (ERPs). For each task, the proposed approach was able to establish a unique sequence of dynamic pattern (observed in all 5 subjects) for brain functional connectivity. We have also introduced and validated a novel time series feature extraction technique, Relative Brain Signature (RBS) that can be applied on ERP signals to provide an effective dimensionality reduction, which does not require the typical channel selection procedure and accounts for all the ERP signals. Unlike common feature extraction techniques, RBS technique obtains information from subjects ERP by considering the status of their relationship to the given population of the study. RBS combines vector space analysis and orthogonal subspace projection to generate feature vectors that signify the corresponding population of the subjects. The proposed technique can be used to identify the biomarkers related to a specific population and to localize functional biomarkers. Furthermore, we have explored the potential prefrontal hemodynamic biomarkers to characterize subjects with Traumatic Brain Injury (TBI) by introducing a novel task-related hemodynamic response detection followed by a heuristic search for optimum set of hemodynamic features. The hemodynamic response from a group of 31 healthy controls and 30 chronic TBI subjects were recorded as they performed a complexity task (i.e. number of events). To identify the hemodynamic signals that show task-related hemodynamic activity, trials with negatively correlated HbO and HbR and HbO larger than HbR were considered for analysis. For identifying the optimum hemodynamic features, unlike common single feature analysis for studying TBI and healthy subjects, we evaluated all possible combinations of multiple hemodynamic features to compare the TBI and healthy populations. Eleven hemodynamic features were extracted from oxygenated hemoglobin (HbO) to determine the optimum set of biomarkers. We investigated the effectiveness of the extracted features in separating TBI and healthy subjects by utilizing a machine learning classification algorithm to score all the possible combinations of features according to their predictive power. The identified optimum feature elements resulted in classification accuracy, sensitivity, and specificity of 85%, 85%, and 84%, respectively. The sensitivity value of 85% suggests that TBI subjects have been successfully characterized for the identified biomarkers with reasonable accuracy. We conducted a spatio-temporal classification to identify regions within the prefrontal cortex (PFC) that contribute in distinguishing between TBI and healthy subjects. As expected, Brodmann areas (BA) 10 within the PFC was isolated as the region that healthy subjects (unlike subjects with TBI), showed major hemodynamic activity in response to the High Complexity task. Overall, our results indicate that identified temporal and spatio-temporal features from PFCs hemodynamic activity are promising biomarkers in classifying subjects with TBI.